In this work, contrary to the standard GP regression setting described above, we do not assume that \(f\)  is sampled from a given GP or that the observation noise is Gaussian. To quantify the estimation error in this more agnostic setting, under Assumption REF , we can rely on Theorem 2 from [1]}, which bounds the regression error with high-probability in the form:
\(P\big [\forall \mathrm {x} \in X, \; |\mu _\mathrm {D}(\mathrm {x}) - f(\mathrm {x})| < \beta (\delta )\sigma _{\mathrm {D}}(\mathrm {x}) \big ]\ge 1-\delta ,\) 
